10 



ELECTRO-MAGNETISM. 



of the magnet may be exactly above 

 the centre of motion. 



In this situation, the action of any 

 electrical current upon the pole S, can 

 have no influence in turning the bar, 



AB, in any particular direction; and 

 the motion of the bar will be determined 

 solely by the action of the current upon 

 the north pole, N. 



(30.) Let A B C D M N O, fig. 13, 



Fig. 13. 



be ihe horizontal circle in which the 

 needle NS revolves, S being the centre 

 of its revolution ; and let W be the ho- 

 rizontal section of the conducting wire, 

 which acts upon the needle, and along 

 which the positive electric current is 

 descending. In every position of the 

 needle, the tangential force, acting upon 

 the pole in the circumference of the 

 circle, takes the direction of a line to 

 the right hand, perpendicular to that 

 which connects the pole and the wire. 

 At D, for instance, it has the direction 

 of the line DC?, perpendicular to DW. 

 Its tendency to produce rotation in the 

 needle, by turning it round S, will 

 be proportional to the cosine of the 

 angle formed between WD and the ra- 

 dius DS ; or it may be represented by 

 the line S d, drawn parallel to WD, and 

 meeting the perpendicular D d, to which 

 it is, of course, also perpendicular ; for 

 it will readily be seen, that the rotatory 

 effect of the force we are considering 

 is the same, whether applied on the 

 needle at D, or at d, on the arm of a 

 lever S d, rigidly connected with the 

 needle. The needle, then, will be urged 

 by this force to move towards V, and as 

 the length of the lever by which it acts 

 continually increases until it reaches this 

 point, so also will the rotatory power 

 increase. After the needle has passed 

 V, it will again diminish ; when it comes 

 to M, its measure is S m, and on arriv- 



ing at N, where the position of the 

 needle NS is at right angles to NW, 

 it is reduced to nothing. This, there- 

 fore, will be a position of equilibrium, 

 and the equilibrium will be a stable one, 

 for, on disturbing the position of the 

 needle by pushing it onwards to O, for 

 example, the rotatory force, in this new 

 position, acts upon it by the lever So, 

 on the opposite side of S m, and, there- 

 fore, tends to give it rotation in the con- 

 trary direction ; that is, to bring the 

 pole of the needle back again to N. 

 After performing a few oscillations, the 

 needle will, therefore, finally settle in 

 the position SN. 



(31.) When the arcs of vibration are 

 small, the forces which tend to bring 

 the needle to its point of rest, are very 

 nearly proportional to the arcs them- 

 selves ; so that, in this respect, its 

 movements are governed by the same 

 law as those of a pendulum. They ac- 

 cordingly furnish very accurate means 

 of determining the comparative intensi- 

 ties of the electro-magnetic forces which 

 act upon the same needle under different 

 circumstances of distance from the wire, 

 or of intensity of the electric current, 

 for the force will always be proportional 

 to the square of the number of oscilla- 

 tions which the needle performs in a 

 given time. (See Treatise on Magnet- 

 ism, 320.) 



(32.) When the needle is still further 



